5.4 Rotational Inertia

Describe the rotational inertia of a rigid system relative to a given axis of rotation.

• Rotational inertia measures a rigid system’s resistance to changes in rotation and is related to the mass of the system and the distribution of that mass relative to the axis of rotation.
• The rotational inertia of an object rotating a perpendicular distance r from an axis is described by the equation =Im r.2
• The total rotational inertia of a collection of objects about an axis is the sum of the rotational inertias of each object about that axis: | AP Physics 1: Algebra-Based Course and Exam Description

Describe the rotational inertia of a rigid system rotating about an axis that does not pass through the system’s center of mass. BOUNDARY STATEMENT AP Physics 1 only expects students to calculate the rotational inertia for systems of five or fewer objects arranged in a two-dimensional configuration. Students do not need to know the rotational inertia of extended rigid systems, as these will be provided within the exam. Students should have a qualitative understanding of the factors that affect rotational inertia; for example, how rotational inertia is greater when mass is farther from the axis of rotation, which is why a hoop has more rotational inertia than a solid disk of the same mass and radius. AP Physics 1: Algebra-Based Course and Exam Description Torque and Rotational Dynamics UNIT 5 TOPIC 5.5 Rotational Equilibrium and Newton’s First Law in Rotational Form

• A rigid system’s rotational inertia in a given plane is at a minimum when the rotational axis passes through the system’s center of mass.
• The parallel axis theorem uses the following equation to relate the rotational inertia of a rigid system about any axis that is parallel to an axis through its center of mass: